Flow velocity out of a rectangluar nozzle

[Seth_eplmf]

Hello, I'm having a hard time coming up with a flow velocity out of a nozzle.

I have a fan that is putting 300 cfm of air through a 3" ID hose. The 3" hose is 45in long, and ends with a rectangular nozzle that has an opening 4.5" x 0.5".

Any help would be greatly appreciated.

 

[Astronuc]

How would one relate volumetric flow rate with duct flow area and mean air velocity?

Does one have to account for compressibility?

 

[Seth_eplmf]

The duct is open at the end, so there is not pressure.

Let me ask this: If you have the nozzle at the end of a hose, would you do the calculation assuming the duct is the size of said nozzle and length doesn't matter (not worried about loss)?

 

[cjl]

How accurate do you need your answer to be? If you know the 300CFM is accurate, you could simply take the cross sectional area of the nozzle and assume uniform flow across the nozzle and get a rough answer that way. The real answer will be a bit faster, since the flow at the walls will be slower (so the central flow needs to be faster to maintain the volumetric flow rate), but I wouldn't bother with that unless you need a very precise answer for some reason.